Guess what: The PM has no power, in law or under the Constitution, to appoint anyone whatsoever, including senators, or judges, or members of cabinet.
Unless you're a strict monarchist, this, like the existence of the PM at all, would fall under the unwritten British imports that came along with that tricky phrase "similar in principle to that of the United Kingdom", no?
Of course, none of that applies to the NDP constitution, since when the CCF was formed, we didn't just put the words "similar in principle to the Liberal Party" in there. That came over time, with leader after leader and council after council making convention a more difficult thing to get any policy through. (The late Saint Jack Layton was responsible for much of this, in fact, with his desire to "modernize" the party by centralizing power in the leader's office and focusing campaigns on such big-ticket economic issues as ATM fees.)